This paper introduces a novel 6D dynamic system derived from modified 3D Lorenz equations of the second type using state feedback control. While the original 3D equations are formally simpler than the classical Lorentz equations, they produce topologically more complex attractors with a two-winged butterfly structure. The proposed system contains the fewest terms compared to existing literature. These terms comprise two cross-product nonlinearities, two piecewise linear functions, six linear terms, and one constant. The new 6D hyperchaotic system exhibits a rich array of dynamic characteristics, including hidden attractors and dissipative behavior. A thorough dynamic analysis of this system was performed. In particular, bifurcation diagrams were constructed, Lyapunov exponents and dimensions were calculated, and multistability and offset boosting control were analyzed to understand the systems behavior further. An electronic circuit of the 6D hyperchaotic two-winged butterfly system was developed in the Multisim computer environment. The designed electronic circuit showed excellent agreement with the simulation results of the new 6D dynamic system. Synchronization of two identical 6D hyperchaotic systems was achieved using the active control method.

Investigating thermal convection within porous media permeated by fluids and micro-organisms stands as a significant inquiry with broad relevance across geophysical and engineering domains. Studying convection within porous media can aid in controlling temperature and nutrient distribution for cell growth and tissue regeneration, as well as the efficiency of biofuel fermentation and production processes. Hence, the primary objective of this study is to investigate the influence of time-periodic gravitational forces on Darcy–Brinkman bio-thermal convection within a porous medium layer. This medium is saturated with a Newtonian fluid that encompasses gyrotactic micro-organisms. The gravity modulation amplitude is assumed to be very small. A weak nonlinear stability analysis is performed to analyze the stationary mode of bioconvection. The heat transport, measured by the Nusselt number, is governed by a non-autonomous Ginzburg–Landau equation. The research explores the influence of several parameters on heat transport, including the Vadaszs number, the modified bioconvective Rayleigh–Darcy number, cell eccentricity, modulation frequency, and modulation amplitude. The results are presented graphically, illustrating the impact of these parameters on heat transfer. The findings reveal that both the Vadaszs number and the modulation amplitude have a positive effect on heat transfer, enhancing the process. On the other hand, an increase in the modified bioconvection Rayleigh–Darcy number and cell eccentricity leads to a decrease in heat transfer. Furthermore, a comparison between the modulated and unmodulated systems indicates that the modulated systems have a more significant influence on the stability problem compared to the unmodulated systems. This highlights the effectiveness of external modulation in controlling heat transport within the system.

The study of thermal convection in porous media saturated by nanofluid and microorganisms is an important problem for many geophysical and engineering applications. The concept of a mixture of nanofluids and microorganisms has attracted the interest of many researchers due to its ability to improve thermal properties and, as a result, heat transfer rates. This property is actively used both in electronic cooling systems and biological applications. Thus, the purpose of this research is to study biothermal instability in a porous medium saturated by a water-based nanofluid containing gyrotactic microorganisms in the presence of a vertical magnetic field. Given the presence of an external magnetic field in both natural and technological situations, we were motivated to perform this theoretical research. Using the Darcy-Brinkman model, a linear analysis of the convective instability has been considered for both-free boundaries, taking into account the effects of Brownian diffusion and thermophoresis. The Galerkin method was used to perform this analytical study. We have established that heat transfer is accomplished by stationary convection without oscillatory movements. In stationary convection regimes, metal oxide nanofluids (Al2O3), metallic nanofluids (Cu, Ag), and semiconductor nanofluids (TiO2, SiO2) are analyzed. Increasing the Chandrasekhar and Darcy numbers improve system stability significantly, but increasing porosity and modified bioconvection Rayleigh-Darcy number speed up the beginning of instability. To determine the transient behavior of heat and mass transports, a non-linear theory based on the representation of the Fourier series method is applied. In small time intervals, the transitional Nusselt and Sherwood numbers exhibit an oscillatory character. The Sherwood numbers (mass transfer) in the time interval reach stationary values faster than the Nusselt numbers (heat transfer). This research might help with seawater convection in the oceanic crust as well as the construction of biosensors.

In this paper, the magnetohydrodynamic (MHD) flow of a ternary hybrid ferrofluid over a stretching/shrinking porous sheet in the presence of radiation and mass transpiration is studied. The ternary hybrid nanofluid is formed by suspending three types of nanoparticles for enhancing heat transfer. The nanoparticles of copper, (Cu) iron oxide (Fe3O4), and cobalt ferrite (CoFe2O4) are suspended in water in this study, producing in the combination Cu-Fe3O4-CoFe2O4-H2O. Brownian motion and thermophoresis are integrated into the ternary hybrid ferrofluid model. Similarity transformations convert the governing partial differential equations into ordinary differential equations. The boundary value problem (BVP) is used in the Maple computer software to solve transformed equations numerically. The computed results for relevant parameters such as velocity profile, temperature profile, skin friction coefficient, local Nusselt and Sherwood numbers are visually shown and explained in detail.

The research is devoted to the stability of convective flow in a nonuniformly rotating layer of an electrically conducting fluid in a spiral magnetic field. The stationary and oscillatory modes of magnetic convection are considered depending on the profile of the angular rotation velocity (Rossby number Ro) and on the profile of the external azimuthal magnetic field (magnetic Rossby number Rb). The non-linear dynamic system of Lorentz type equations is obtained by using the Galerkin method. Numerical analysis of these equations has shown the presence of chaotic behavior of convective flows. The criteria of the occurrence of chaotic movements are found. It depends on the parameters of convection: dimensionless numbers of Rayleigh Ra, Chandrasekhar Q, Taylor Ta, and external azimuthal magnetic field with the Rossby magnetic number Rb for Rayleigh (Ro = −1) and Kepler ( Ro = − 3 / 4 ) profiles of the angular rotation velocity of the medium.

This paper presents a novel four-dimensional (4D) memristive system, notable for its simplicity and unique dynamic behaviors. Comprising only seven terms and devoid of equilibrium points, this system is capable of generating hidden attractors. A comprehensive analysis of its dynamic properties is conducted, including Lyapunov exponents, Kaplan–Yorke dimensions, temporal diagrams and phase portraits, multistability, and offset boosting. Numerical simulations over a sufficiently long time interval show that the Lyapunov function remains bounded, thereby confirming the dissipative nature and global stability of the newly proposed 4D hyperchaotic system. The theoretical model is further validated through electronic simulations of the chaotic system using Multisim software. Additionally, the paper explores synchronization between two identical 4D hyperchaotic systems. The proposed system, despite its structural simplicity, exhibits intricate chaotic dynamics, making it suitable for various practical applications. In particular, a method for chaotic encryption and decryption of an information signal was developed and validated through numerical testing. Based on the method of complete synchronization of chaotic systems, the possibility of detecting a weak signal is demonstrated. The proposed system is also implemented on an Arduino UNO to demonstrate its practical applicability for real-time chaotic signal generation and image encryption.